4. Let TB:R" + R" and TA: RM → RP be the linear transformations represented by...
25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R – RM is defined by Tv) = Av, where A is as follows. 0 1 -6 1 -1 7 40 0 1 9 1 (a) Find T(0, 3, 2, 1). STEP 1: Use the definition of T to write a matrix equation for TO, 3, 2, 1). T10, 3, 2, 1) = and STEP 2: Use your result from Step 1 to solve for T(0, 3, 2, 1). Ti0,...
s={(8.60) :) :) is a basis of M3x2(R)? (d) (1 point) The set = {(1 9:(. :) : 6 1) (1 1) (1 :) :()} is linearly independent. (e) (1 point) For a linear transformation A:R" + Rd the dimension of the nullspace is larger than d. (f) (1 points) Let AC M4x4 be a diagonal matrix. A is similar to a matrix A which has eigenvalues 1,2,3 with algebraic multiplicities 1,2, 1 and geometric multiplicities 1,1, 1 respectively. 8....
Problem 25 please -Sesin(2x)-9ecos(2x). 21. W = Span(B), where Br(x2e-4x , xe®, e-4x); f(x)--5x2r" + 2e-4-1e 22. W= Span(B),where B= ({x25, x5*, 5x)); f(x)--4x2 5x+9s5x-2(5x). 3 W Span(B), where B (Exsin(2x), xcos(2x), sin(2x), cos(2x)y): f(x) = 4x sin(2x) + 9x cos(20-5 sin(2x) + 8 cos(2x). 24, In Exercise 21 of Section 3.6, we constructed the matrix [D, of the derivative operator D on W- Span(B), where B e sin(bx), e" cos(bx)): Dls a a. Find [D 1g and [D'lg: Observe...